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Difficulty: MediumNewton's Laws of Motion and Linear Momentum

If two objects of unequal mass experience the same magnitude of net force for the same duration of time, the lighter object will undergo a greater change in linear momentum than the heavier object.

Answer: Answer

Answer

The statement is False. Both objects undergo the exact same change in linear momentum because impulse depends only on the force applied and the time duration, not on the mass of the object.
The statement is false because the change in momentum (Δp\Delta p) is determined solely by the impulse applied (FΔtF \Delta t). Since the net force and time duration are identical for both objects, the change in momentum is the same for both, regardless of mass differences.

Step-by-Step Solution

1
State the relationship between force, time, and momentum change using Newton's Second Law.
Impulse J=FΔt=ΔpJ = F \Delta t = \Delta p, where FF is the net force, Δt\Delta t is the duration, and Δp\Delta p is the change in linear momentum.
The impulse-momentum theorem directly links the net force acting over time to the resulting change in momentum.
2
Evaluate the given problem constraints for both the lighter mass (m1m_1) and heavier mass (m2m_2).
F1=F2=FF_1 = F_2 = F and Δt1=Δt2=Δt\Delta t_1 = \Delta t_2 = \Delta t.
Both objects experience equal forces for equal durations.
3
Compare the resulting changes in linear momentum.
Δp1=FΔt\Delta p_1 = F \Delta t and Δp2=FΔt\Delta p_2 = F \Delta t, so Δp1=Δp2\Delta p_1 = \Delta p_2.
Because mass mm does not alter the product FΔtF \Delta t, both objects experience identical momentum changes.

Key Concept

Impulse-Momentum Theorem and Newton's Second Law of Motion
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Topics

Newton's Laws of Motion and Linear Momentum

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